Physics 4A Recitation Problems
8/18/2008
1. While standing in an elevator you see a screw fall
from the ceiling as it moves upward at a constant
speed of 2.2 m/s. The elevator ceiling is 3 m
above the floor. How long is the screw in the air?
Is there more than one way to solve it? What if
aE=2.2m/s2 (up) & vE=2.2m/s when screw falls?
2. An object travels at a constant rate of 3.0 m/s
from t=0.0 s to t=3.0 s. It then accelerates at 1.0
m/s2 over the next 2.0 s. Then it accelerates at 2.0 m/s2 over the next 2.0 s. For the last 3.0 s, its
position remains the same. Sketch v vs. t, a vs. t,
and s vs. t over the 10.0 s interval.
3. An inquisitive physics student and mountain
climber climbs a 51.0 m cliff that overhangs a
calm pool of water. He throws two stones
vertically downward, 1.00 s apart, and observes
that they cause a single splash. The first stone
has an initial speed of 2.00. m/s downward.
a. How long after release of the first stone do the
two stones hit the water?
b. What initial velocity must the second stone
have if they are to hit simultaneously?
c. What is the speed of each stone at the instant
the two hit the water?
Physics 4A Recitation Problems
8/18/2008
1. A jet airliner moving initially at 330 mph due east
enters a region where the wind is blowing at 80
mph in a direction 30.0° north of east. Determine
the new speed and direction of the aircraft
relative to the ground.
2. A pitcher throws a fastball. The ball is released
horizontally from the pitcher's mound when the
hand of the pitcher is at an elevation of 1.7 m
above the level field. The catcher catches the ball
19.5 m away at an elevation of 0.90 m above the
ground. Calculate the initial speed of the ball as it
left the pitcher's hand.
3. A ball is tossed from an upper-story window of a
building. The ball is given an initial velocity of
8.20 m/s at an angle of 15.0° below the horizontal.
It strikes the ground 3.00 s later.
a. How far horizontally from the base of the
building does the ball strike the ground?
b. Find the height from which the ball was
thrown.
Physics 4A Recitation Problems
8/18/2008
1. What are the forces acting on a person in an
elevator accelerating upward? What are the
forces acting on the elevator? What are the forces
acting on the system defined by the person and
elevator?
2. Consider the system below. The 10.0N force only
acts on the top object only. There is a frictional
force between M1 and M2 and between M2 and the
table supporting M2. Draw a separate free-body
diagram for each object. You must indicate all
forces acting on the objects using words only (no
labels).
F=10.0N
M1
M2
3. A block and incline plane are placed in an
elevator that is moving upward at a constant
speed v=2m/s. What is its acceleration? What if it
is accelerating upward at 2m/s2?
θ
Physics 4A Recitation Problems
8/18/2008
Physics 4A Recitation Problems
8/18/2008
Physics 4A Recitation Problems
8/18/2008
4. A painter weighing 128 lb stands on a 32lb
bosun’s chair to paint a house. To get started
she accelerates herself and the chair at a rate of
2ft/s2. With what force must she pull on the rope?
What is the force on the pulley? After 1 s she
pulls so that she and the chair go up at a
constant speed of 2ft/s. With what force must she
pull on the rope (refer to problem 5-51)?
5. A coin placed 31.0 cm from the center of a
rotating, horizontal turntable slips when its
speed is 50.9 cm/s. What is the coefficient of
static friction?
Physics 4A Recitation Problems
8/18/2008
6. Jill pushes an 8.0kg box is through a distance of
8.0m up a 20o frictionless incline. The applied
force is parallel to the incline.
a. What is the work done by the normal force and
gravity?
b. If the box is pushed at a constant speed of
2.0m/s, what is the force applied by Jill?
c. Suppose that she decides to double the
applied force over the next 4.0m. How fast will
the box be moving after applying the larger
force?
7. Consider the motion of an object from (0,0) to
(0,1) over the two paths shown. If the applied
F=3xyi+3y2j, calculate the work done by the force
on the object over the three paths.
y
(0,1)
^idx
^jdy
^jdy
(0,0)
(1,1)
^idx
(1,0)
x
Physics 4A Recitation Problems
8/18/2008
Physics 4A Recitation Problems
8/18/2008
Physics 4A Recitation Problems
8/18/2008
Physics 4A Recitation Problems
8/18/2008
8. A 10.0 kg watermelon is launched off a 30.0m
tower. Its initial velocity is 20.0m/s at 30 degrees
above the horizontal. Find its speed when it hits
the ground. Does the launch angle matter?
9. A light, rigid rod is 77.8 cm long. Its top end is
pivoted on a low-friction horizontal axle. The rod
hangs straight down at rest with a small massive
ball attached to its bottom end. You strike the
ball, suddenly giving it a horizontal velocity so
that it swings around in a full circle. What
minimum speed at the bottom is required to
make the ball go over the top of the circle?
10. The Atwood machine shown has two masses,
m1 = 4.0 kg and m2 = 2.0 kg. The initial height
above the ground of m1 is 2 m. What is the
speed of m1 just before impact with the ground?
1
1
2
2
Physics 4A Recitation Problems
8/18/2008
11. A 1.0 kg block slides down an incline (30°) a
distance of 1 m where it slams into a spring (k =
100 N/m). If µ k = 0.2, what is the speed of the
mass after the spring is compressed by 0.1 m?
Physics 4A Recitation Problems
8/18/2008
12. A mass M is hung from a two-step pulley as
shown below. The pulley is composed of two
disks of radius R1 and R2 and rotational inertia I1
and I2 , respectively. The string is wound around
the pulley and the mass is released. Calculate
the acceleration of the falling mass M.
R2
M
13. A disk rolls down an incline plane of angle α.
Calculate its acceleration. Solve it in more than
one way.
Physics 4A Recitation Problems
8/18/2008
14. A 1 kg ball traveling at 1 m/s perpendicular to a
1 kg thin rod 2 m in length that is at rest,
undergoes an elastic collision with the end of
the rod. What are the linear velocities of the ball
and the rod and the angular speed of the rod
after the collision? (Hint: the ball’s path is
unchanged after the collision.)
15. A solid ball (pool cue) is struck by a stick as
shown below. Its velocity is vo just after the
interaction. Because of its “forward english” the
velocity of its center of mass is 9/7 vo when it
rolls without slipping. Find h the point where it
was is struck (with respect to its center)?
F
h
R
16. Consider an Atwood’s machine with masses
M1>M2 tied to strings. The pulley has mass MP
and radius R. Calculate the acceleration of the
masses. Solve it in more than one way.
Physics 4A Recitation Problems
8/18/2008
17. Consider two masses connected by a light rod
of length d and rotating about a vertical axis
with as angular speed w shown below.
R
→
L
φ
φ
2
R
→
v
ω
→
v
1
Physics 4A Recitation Problems
8/18/2008
18. Assume a person bends forward to lift a load
"with his back" as shown in the figure below. The
person's spine pivots mainly at the fifth lumbar
vertebra, with the principal supporting force
provided by the erector spinalis muscle in the
back. To estimate the magnitude of the forces
involved, consider the model shown in the figure
for a person bending forward to lift a 200-N
object. The person's spine and upper body are
represented as a uniform horizontal rod of weight
350 N, pivoted at the base of the spine. The
erector spinals muscle, attached at a point two
thirds of the way up the spine, maintains the
position of the back. The angle between the
spine and this muscle is 12.0°. Find the tension
in the back muscle and the compression force in
the spine (2710N 2650N). Is it wise to lift with
your back?